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A057708
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Numbers m such that 2^m reversed is prime.
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14
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1, 4, 5, 7, 10, 17, 24, 37, 45, 55, 70, 77, 107, 137, 150, 271, 364, 1157, 1656, 2004, 2126, 3033, 3489, 3645, 4336, 6597, 7279, 12690, 13840, 20108, 21693, 28888, 84155, 102930
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OFFSET
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1,2
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COMMENTS
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If m is an even term, then u = m/2 is a term of A350441, this because 2^m = 4^(m/2). In fact, terms of A350441 are half the even terms of this sequence here.
If m is a term multiple of 3, then k = m/3 is a term of A350442, this because 2^m = 8^(m/3). First examples: m = 24, 45, 150, 1656, ... and corresponding k = 8, 15, 50, 552, ... (End)
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LINKS
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EXAMPLE
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4 is a term because 2^4 reversed is 61 and prime.
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MAPLE
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with(numtheory): myarray := []: for n from 1 to 4000 do it1 := convert(2^n, base, 10): it2 := sum(10^(nops(it1)-i)*it1[i], i=1..nops(it1)): if isprime(it2) then printf(`%d, `, n) fi: od:
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MATHEMATICA
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Do[ If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[2^n]] ]], Print[ n]], {n, 20000}] (* Robert G. Wilson v, Jan 29 2005 *)
Select[Range[4400], PrimeQ[IntegerReverse[2^#]]&] (* Requires Mathematica version 10 or later *) (* The program generates the first 25 terms of the sequence; to generate more, increase the Range constant, but the program will take longer to run. *) (* Harvey P. Dale, Aug 05 2020 *)
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PROG
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(Python)
from sympy import isprime
while k <= 10**3:
if isprime(int(str(m)[::-1])):
k += 1
(PARI) isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ Mohammed Yaseen, Jul 20 2022
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CROSSREFS
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KEYWORD
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base,nonn,more
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AUTHOR
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EXTENSIONS
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More terms from Chris Nash (chris_nash(AT)prodigy.net), Oct 25 2000
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STATUS
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approved
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